Childbirth is a biological process that is normal, but also takes a toll on the psychological and mental health of both parents. Though men hardly show their emotions, but if you've met a man who lost a child and seen how broken he was, you will understand that the pain and joy of nurturing a child doesn't only depend on the mother.
The man also deserves leave because childbearing is a family thing, both the mother and child need the man's support, care, and protection, as well as a great bond as a family, not just a mother-to-child bond, but rather a parent-to-child bond.
Also "not showing emotions" isn't a good reason, that's just enforcing bad stereotypes. Women are traditionally encouraged to do that from the start. Men need to be trusted to learn that and encouraged to do so. Also it's not just about showing emotions, but listening and trying to understand to others and accepting their emotions (aka empathy).